The Riesz composition identity \(\kappa _\alpha =\kappa _{\alpha /2}\ast \kappa _{\alpha /2}\)  [1]} (cf. also [2]}) implies that the kernel \(\kappa _\alpha \)  is strictly positive definite, which means that for any (signed) \(\mu \in \mathfrak {M}\) , the \(\alpha \) -Riesz energy
\(\kappa _\alpha (\mu ,\mu ):=\int \kappa _\alpha (x,y)\,d(\mu \otimes \mu )(x,y)\) 
